Name: Nathan Urban
Pronouns:
Biography:
I work in applied mathematics at Brookhaven National Laboratory. I have a Ph.D. in computational condensed matter physics (Penn State) and undergraduate degrees in physics, mathematics, and computer science (Virginia Tech). I have held postdoctoral appointments at Penn State and Princeton and a staff position as Los Alamos National Laboratory. I have worked extensively in the fields of climate impacts science and more recently in biomedicine, materials science, accelerator physics, quantum computing, and others. My research areas include Bayesian statistics and uncertainty quantification (with an emphasis on model structural or multi-model uncertainties / model-form errors), decision making under uncertainty, data-model fusion and information fusion, model reduction / model emulation / surrogate modeling, scientific machine learning / hybrid numerical physics+machine learning models, optimization, optimal experimental design, design and control of experimental and model workflows, and scalable data analysis.
Institution/Lab: Brookhaven National Laboratory
Website: https://www.bnl.gov/staff/nurban/
SRP Collaboration Topic/Title: Neural partial differential equations
Field or research area: Applied mathematics
Please select all the topical areas that apply to your project:
Computational Science Applications (i.e., bioscience, cosmology, chemistry, environmental science, nanotechnology, climate, etc.); Data Science (i.e., data analytics, data management & storage systems, visualization); High-Performance Computing; Machine Learning and AI
Brief Abstract:
Numerical computer simulation models are used to predict the behavior of physical systems such as fluids or materials. These simulations are based on underlying partial differential equations (PDEs). Neural partial differential equations (NPDEs) are a machine learning (ML) approach that replaces these physical governing equations with a neural network. This ML approach is used when the equations describing a system’s behavior are not fully understood from a physical perspective, because it permits (1) learning unknown governing equations from data, and (2) quantifying uncertainties in the mathematical form of learned equations. “”Hybrid”” simulations are also possible, with some of the equations specified from physical principles and others learned from data as neural networks. In this project, we will explore the potential for NPDEs to describe various physical systems, such as the heat diffusion equation, or more complex systems like the reaction-diffusion equations describing spatially-distributed chemical reactions, or the Cahn-Hilliard equations describing phase separation in self-assembling nanomaterials. This can include studying the ability of the neural network to emulate the behavior of the original system, as well as Bayesian statistical and mathematical dimension reduction methods to efficiently quantify uncertainties of the NPDE in a reduced-dimensional space of neural network parameters.
Desired relevant skills, background, or interests:
Scientific programming Mathematics (ideally at the level of differential equations, linear algebra, or multivariate calculus)
Other comments:
Do any special requirements apply? In-Person Only; Permanent Resident OK; International OK
Other, specify:
Keywords:
statistical uncertainty quantification; scientific machine learning; differential equations; dynamical systems; modeling and simulation
Lightning Talk Title: Learning Predictive Physical Models